Note: Start the potatoes the day before you plan to serve the salad so they have time to rest in the fridge overnight.
Preheat oven to 350 degrees. In a large pot of heavily salted water, bring potatoes to a boil over high heat; reduce heat to low and simmer until cooked through, about 12 minutes. Drain potatoes and transfer to a rimmed baking sheet. With the bottom of a heavy jar or glass, crush each potato slightly, just so the skin splits. Dry potatoes in oven for 10 minutes, and then transfer to a large bowl. Salt generously and sprinkle with vinegar and lemon juice. Let potatoes cool briefly and then transfer to a zip-top bag. Refrigerate overnight.
In a large bowl, combine potatoes with smoked paprika and mayonnaise and stir to coat. Fold in scallions and cilantro, and serve.